Geotechnical Engineering

DHARM

454 GEOTECHNICAL ENGINEERING

If a structure such as a retaining wall of height H is interposed from the surface and

imagined to be held without yield, the total thrust on the wall unit length P 0 , is given by

P 0 = σγγh

H H

.....dz==zz K 00 z dz K H^2

0 0

1

2

...(Eq. 13.6)

This is considered to act at (1/3) H above the base of wall. As has been indicated in the
previous chapter, choosing an appropriate value for the Poisson’s ratio, ν, is by no means easy;
this is the limitation in arriving at K 0 from equation 13.4.

Various researchers proposed empirical relationships for K 0 , some of which are given

below:

K 0 = (1 – sin φ′) (Jaky, 1944) ...(Eq. 13.7 (a))

K 0 = 0.9 (1– sin φ′) (Fraser, 1957) ...(Eq. 13.7 (b))

K 0 = 0.19 + 0.233 log Ip (Kenney, 1959) ...(Eq. 13.7 (c))

K 0 = [1 + (2/3) sin φ′]

1

1

−

+

F

HG

I

KJ

sin

sin

φ

φ

(Kezdi, 1962) ...(Eq. 13.7 (d))

K 0 = (0.95 – sin φ′) (Brooker and Ireland, 1965) ...(Eq. 13.7 (e))

φ′ in these equations represents the effective angle of friction of the soil and Ip, the plasticity

index. Brooker and Ireland (1965) recommend Jaky’s equation for cohesioness soils and their

own equation, given above, for cohesive soils. However, Alpan (1967) recommends Jaky’s equa-

tion for cohesionless soils and Kenney equation for cohesive soils as does Kenney (1959). Cer-

tain values of the coefficient of earth pressure at rest are suggested for different soils, based on

field data, experimental evidence and experience. These are given in Table 13.1.

Table 13.1 Coefficient of earth pressure at rest

S.No. Soil K 0

1 Loose Sand (e = 0.8)

dry ... 0.64

Saturated ... 0.46

2 Dense sand (e = 0.6)

dry ... 0.49

saturated ... 0.36

3 Sand (compacted in layers) ... 0.80

4 Soft clay (Ip = 30) ... 0.60

5 Hard clay (Ip = 9) ... 0.42

6 Undisturbed Silty clay (Ip = 45) ... 0.57

13.5 Earth Pressure Theories

The magnitude of the lateral earth pressure is evaluated by the application of one or the other

of the so-called ‘lateral earth pressure theories’ or simply ‘earth pressure theories’. The prob-

lem of determining the lateral pressure against retaining walls is one of the oldest in the field

of engineering. A French military engineer, Vauban, set forth certain rules for the design of